'Your family won't get you a job or pay your bills ... By contrast, distant contacts are sometimes surprisingly useful'

This may be a statement of the obvious at Christmas, but our families can sometimes let us down. Evidence comes from a little-noticed survey published by the US Census Bureau in September. The findings are conveyed in a sad and simple graph. It reports a survey of "households experiencing hardship" in 2011 - and who helped them when times were tough. What counted as tough times? Having a phone disconnected, missing utility bill payments, falling into rent or mortgage arrears, or not seeing a doctor or dentist when needed.

More than half of such households expected help from family members, as did almost half from friends. Rather fewer - about a fifth - hoped for help from a social agency, charity or church.

The overwhelming majority were disappointed. It was rare for family members to provide help with rent arrears - about one time in six - and it was rarer still to receive financial help from other sources or for other purposes.

In short, hard-up Americans were confident of help in need from those close to them - and that confidence was misplaced. (If you're looking for an explanation of the popularity of payday loans, this finding isn't a bad start.)

An optimistic reading of this research is that there are plenty of people whose families or friends did help them and thus never featured in the sample. Perhaps. But as the economist Timothy Taylor comments, enough people experience disappointment to leave "lasting shadows".

This dispiriting stuff reminded me of Mark Granovetter's work on "the strength of weak ties", published in 1973. Granovetter, a sociologist, brought together two disparate strands of work: a survey of how people with professional or managerial jobs had found those jobs; and a theoretical analysis of the structure of social networks.

Start with the theoretical observation first: the most irreplaceable social connections, paradoxically, are often rather weak or distant ones. A family group or clique of close friends all tend to know each other and know similar things at similar times. Their social ties are strong but also redundant, in the sense that there are many different paths through which information could pass from one member of that group to another.

By contrast, "weak ties" between one social cluster and another are valuable precisely because the social contact is unusual. Information passed along a weak tie will often be totally new - and if it doesn't arrive through the weak tie, it is unlikely to arrive at all.

Granovetter then supplemented this theoretical idea with his survey, showing that it was very common for people to find jobs - especially managerial jobs and jobs with which they were satisfied - through personal contacts. The old saw is true: it's not what you know, it's who you know. Or as Granovetter put it in his book Finding a Job, what matters most is "one's position in a social network".

But this is not because of crude nepotism: the key contacts who helped jobseekers find jobs were typically distant rather than close friends - old college contacts, perhaps, or former colleagues. Granovetter's analysis made this finding make sense: it's the more peripheral contacts who tell you things you don't already know.

More recent research - for instance, a "big data" analysis of millions of mobile phone records conducted by Jukka-Pekka Onnela, Albert-LГЎszlГі BarabГЎsi and others - has backed up Granovetter's argument that the weaker ties are the vital ones.

It's a disappointing message to deliver at Christmas: your family won't get you a job or pay your bills - count yourself lucky if they serve you a slice of turkey. By contrast, distant contacts are sometimes surprisingly useful: no wonder we send Christmas cards to people we barely remember.

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